Optimization algorithm and options

This chapter summarizes the optimization scheme that is used to solve the optimization problem in Problem formulation and implementation. This includes the basic algorithm as well as the options that can be adjusted by the user. Note that all options as well as their corresponding default values are listed in Table Algorithmic Options.. The setting of the options is detailed in Usage of GRAMPC for usage in C and Matlab.

• Optimization algorithm
  • Augmented Lagrangian method
  • Projected gradient method
  • Algorithmic structure
• Numerical Integration
  • Integration of cost functional and explicit ODEs
  • Integration of semi-implicit ODEs and DAEs (RODAS)
• Line search
  • Adaptive line search
  • Explicit line search
  • Fallback strategy for explicit line search
• Update of multipliers and penalties
  • Update of Lagrangian multipliers
  • Update of penalty parameters
  • Estimation of minimal penalty parameter
• Convergence criterion
• Scaling
• Control shift
• Status flags